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  4. If x1 , x2 , ..., xn and (1/h1) , (1/h2) , ... , (1/hn) are two A.P.s such that x3 = h 2 = 8 and x8 = h7 = 20, then x5 ⋠h10 equals :

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Q. If $x_1 , x_2 , ..., x_n$ and $\frac{1}{h_1} , \frac{1}{h_2} , ... , \frac{1}{h_n}$ are two A.P.s such that $x_3 = h _2 = 8$ and $x_8 = h_7 = 20$, then $x_5 ⋅ h_{10}$ equals :

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Solution:

$x_{1}, x_{2}, x_{3}, \dots\dots.. x_{n}$ in AP.
$x_{3} = 8\quad\&\quad x_{8} = 20\quad\Rightarrow \,x_{5} = \frac{64}{5}$
$h_{1}, h_{2}, h_{3}, \dots\dots\dots h_{n},$ in HP
$h_{2} = 8,\quad h_{7} = 20\quad\Rightarrow \quad h_{10} = 200$
$\Rightarrow \,\,x_{5} h_{10} = \frac{64}{5}\times200 = \frac{12800}{5} = 2560$